The manner of operation of a laser beam amplification device is briefly recalled. It mainly comprises an amplifying medium and pumping sources which inject energy into the amplifying medium. This amplifying medium which has the shape of a bar may be a crystal, or else a doped glass. Thereafter, the laser beam to be amplified traverses the amplifying bar one or more times by means of optical devices with mirrors for example; on each pass it extracts a part of the energy injected during the pumping and is thus amplified in the amplifying bar. For an amplifying bar of cylindrical shape, the energy deposited during pumping is generally confined in the central part, delimited by the diameter D of the pump beam, of the amplifying bar. Part of the energy deposited during pumping is not converted into luminous energy but into thermal energy in the amplifying medium; this thermal energy must be removed by means of a cooling device (based on water for example), which will have to be all the more effective the higher the thermal power (product of the thermal energy and the pulse repetition rate of the laser).
On this type of configuration of laser beam amplification device, a parasitic phenomenon called transverse lasing arises between the deposition of energy in the amplifying bar by optical pumping and its extraction by the beam to be amplified.
This phenomenon is related to the creation in the amplifying bar of a laser sub-cavity along an axis transverse to the longitudinal axis of the amplifying bar, the breaks in refractive index at the amplifying bar-environment interface ensuring the function of mirrors of this sub-cavity. Transverse lasing occurs when the oscillation condition for this sub-cavity is satisfied, that is to say when there is conservation of the energy over an outward-return trip within the sub-cavity, or stated otherwise when the transverse gain G compensates for the losses P of the sub-cavity.
Hereinafter, a crystal is taken as exemplary amplifying bar; it can of course be replaced with doped glass.
Represented in FIG. 1 is the transverse optical gain G in a cylindrical amplifying crystal 1 pumped along the longitudinal axis Ox of the crystal, by its two faces S1, S2 by a pumping laser beam 3 of diameter D. The pumping laser is typically a solid laser or a fiber laser or a laser diode. If g0 designates the lineal density of gain, the small-signal gain gps is equal to g0.e in the longitudinal direction Ox and to g0.D in a transverse direction perpendicular to Ox. We commonly have D≧e (the quantities are not to scale in the figure so as to facilitate the reading of the gain curve); the length e of the crystal is typically between 2 and 5 cm, and the diameter D between 5 and 20 cm.
The optical gain G being proportional to egps, we have:eg0.D>>eg0.e 
The optical gain G in the transverse direction is therefore much larger than the optical gain G in the longitudinal direction, that is to say in the direction of the laser beam to be amplified.
Transverse lasing is manifested as a strong evacuation of the energy stored in the crystal, caused by unchecked transverse stimulated emissions, at the expense of the laser beam that it is desired to amplify.
This transverse lasing is particularly troublesome in the case of solid amplifying media with high gains and of large dimensions (typically a gain g0 of 0.88 and a pump diameter of 70 mm). It prevents for example the generation of femtosecond laser pulses of very significant peak power, typically of the order of a petawatt, on the basis of a TI:Sapphire crystal pumped at high energies of the order of 100 J.
Hitherto, parasitic lasing was suppressed by increasing the losses P for the parasitic beam by placing on the periphery of the crystal a material which is absorbent at the fluorescence wavelength of the crystal; in order for the device to be fully effective it is moreover necessary that the refractive index of the crystal and that of the absorbent material be as close as possible so as to avoid appreciable reflection at the crystal interface—which absorbent material would lead to the occurrence of parasitic lasing. This may for example be achieved by means of an absorbent liquid in which the surface Σ connecting the faces S1 and S2 of the crystal is immersed. This solution is described in patent application FR 2 901 067. The liquid used comprises a solvent whose refractive index is close to that of the crystal, and a dye which is absorbent at the fluorescence wavelength of the crystal. The material used may also be a solid as described in the publication “Production of >1021 W/cm2 from a large-aperture Ti:sapphire laser system” by J D Bonlie et al (Applied Physics B (Lasers and Optics)) Springer-Verlag Germany, vol B70 June 2000.
In the case of a TI:Sapphire amplifying crystal, the refractive index n is equal to 1.76. To increase the losses at the interface with a liquid, the index of the liquid used must be close to that of the crystal; the two indices are considered to be close if their difference of index is less than or equal to 0.01. This liquid substitutes for the water customarily surrounding the crystal, whose function is to remove the thermal power generated in the crystal by the pumping process. It must therefore also ensure this function of removing the thermal power in addition to the function of suppressing the transverse lasing; now, the thermal properties and first and foremost the heat capacity of liquids of this type are well shy of those of water, thereby rendering them inoperative when the laser repetition rate and as a consequence the mean thermal power are high, typically above 1 Hz for an amplifier of high energy, that is to say greater than 30 Joules. This liquid is moreover very corrosive. It is furthermore expensive and toxic and therefore dangerous to use; it deteriorates over time.
Consequently, there still remains a need for a device that simultaneously satisfies all the aforementioned requirements, in terms mainly of suppression of transverse lasing and removal of the mean thermal power for appreciable values of these (typically greater than 100 Watts) but also of safety of use and of robustness over time.